%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:22:53 AM UTC 2026
% Result : Theorem 3.44s 2.11s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 3 def)
% Number of atoms : 37 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 54 ( 2 ~; 0 |; 0 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 13 ^; 6 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mequiv_decl,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(set_equal_decl,type,
set_equal: $i > $i > mworld > $o ).
thf(element_decl,type,
element: $i > $i > mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( set_equal @ A @ B ) @ ( set_equal @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( set_equal @ A @ B ) @ ( set_equal @ B @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i,B: $i] :
( ( set_equal @ A @ B @ mactual )
= ( set_equal @ B @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( set_equal @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mequiv @ ( element @ C @ A ) @ ( element @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43_1) ).
thf(7,plain,
! [A: $i,B: $i] :
( ( set_equal @ A @ B @ mactual )
= ( ! [C: $i] :
( ( element @ C @ A @ mactual )
= ( element @ C @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
$false,
inference(e,[status(thm)],[4,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:34:25 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.02/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.01 % [INFO] Parsing done (206ms).
% 1.18/1.02 % [INFO] Running in sequential loop mode.
% 2.11/1.44 % [INFO] eprover registered as external prover.
% 2.11/1.44 % [INFO] Scanning for conjecture ...
% 2.30/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.49/1.60 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.49/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.49/1.61 % [INFO] Type checking passed.
% 2.49/1.62 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.44/2.10 % External prover 'e' found a proof!
% 3.44/2.10 % [INFO] Killing All external provers ...
% 3.44/2.10 % Time passed: 1752ms (effective reasoning time: 1075ms)
% 3.44/2.11 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.44/2.11 % Axioms used in derivation (1): pel43_1
% 3.44/2.11 % No. of inferences in proof: 6
% 3.44/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1752 ms resp. 1075 ms w/o parsing
% 3.71/2.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.71/2.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------